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nathanl6656
Benutzername
nathanl6656
Punkte
413
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98
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19
98 Questions
19 Answers
+1
3
1
+413
Algebra
Suppose the polynomial p(x)=x^3+ax^2+bc+c has the property that the mean of its zeroes, the product of its zeroes, and the sum of its coefficients are all equal. If the y-intercept of the graph of y=p(x) is 0, what is b?
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nathanl6656
02.03.2025
0
4
1
+413
Algebra
Find all (real or nonreal) x satisfying
(x - 3)^4 + (x - 5)^4 = -8 + 6(x - 3)(x - 5)^3 - 11(x - 3)^3 (x - 5).
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nathanl6656
02.03.2025
0
2
1
+413
Algebra
Express x^8 + x^4 y^4 - x^6 y^2 + x^3 y^5 - 4xy^7 - y^8 as the product of two polynomials of degree 2, and a polynomial of degree 4.
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nathanl6656
02.03.2025
0
3
1
+413
Algebra
Find the constant k so that
2x^2 + 5xy - 8y^2 + 7x + 25y + k
can be expressed as the product of two linear factors of the form ax + by + c.
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nathanl6656
02.03.2025
0
4
0
+413
Algebra
Solve the system of equations
x + y + 2z = 1
-2x - 4y + 2z = 7
10x - 17x + 13z = 8
mehr ..
nathanl6656
22.02.2025
0
6
0
+413
Algebra
Solve the system of equations
5x + 3z = 1
-x + y - z = 0
2x - 3y + 7z = -4
nathanl6656
22.02.2025
0
3
0
+413
Algebra
Given that
5a - 7b + 3c = 19
4a + 2b - 8c = 4
7a + 5b + 3c = -11
mehr ..
nathanl6656
22.02.2025
0
4
0
+413
Algebra
Find all values of z such that z^4 - 4z^2 + 3 = 5z^2 + 11z^3 - 40.
nathanl6656
22.02.2025
0
12
0
+413
Counting
At a meeting, $5$ scientists, $2$ mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if each scientist must sit next to a mathematician? (Two seatings are considered equivalent
mehr ..
nathanl6656
23.01.2025
0
12
0
+413
Counting
Four children and four adults are to be seated at a circular table. In how many different ways can they be seated if all the children are next to each other, and all the adults are next to each other? (Two seatings are considered the same if
mehr ..
nathanl6656
23.01.2025
0
9
1
+413
Counting
I have $4$ different mathematics textbooks and $3$ different psychology textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if there must be a mathematics textbook exactly in the middle, and all the psychology textbooks are
mehr ..
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nathanl6656
23.01.2025
0
11
1
+413
Algebra
A line bisects the area of the square below. The slope of the line is 3, and its y-intercept is (0,b). Find $b.$
The vertices of the square are (-4,-4), (-4,4), (4,4), and (4,-4).
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nathanl6656
01.01.2025
0
12
1
+413
Algebra
Find the coordinates of the intersection of the diagonals of quadrilateral ABCD, where:
A(3, 6), B(9, 6), C(7, 3), and D(1, 1).
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nathanl6656
01.01.2025
0
15
1
+413
Algebra
The graph x^2+y^2=121 intersects y=8x+10 at two points P and Q. Find PQ.
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nathanl6656
01.01.2025
0
14
1
+413
Algebra
The line 3x-4y=5 intersects the $x$-axis and $y$-axis at points $A$ and $B,$ respectively. Find the distance $AB.$
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nathanl6656
01.01.2025
0
19
1
+413
Geometry
Two tangents $\overline{PA}$ and $\overline{PB}$ are drawn to a circle, where $P$ lies outside the circle, and $A$ and $B$ lie on the circle. The length of $\overline{AB}$ is $4,$ and the circle has a radius of $5.$ Find the length $AB.$
mehr ..
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nathanl6656
13.12.2024
0
20
0
+413
Geometry
Lines $XQ$ and $XR$ are tangent to a circle, as shown below. If $\angle XTU = 47^\circ$ and $\angle QAU = 65^\circ,$ then find $\angle QXR,$ in degrees.
nathanl6656
13.12.2024
0
17
1
+413
Geometry
A circular table is pushed into a corner of the room, where two walls meet at a right angle. A point P on the edge of the table (as shown below) has a distance of 6 from one wall, and a distance of 6 from the other wall. Find the radius of the
mehr ..
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nathanl6656
13.12.2024
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